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X OP MATHEMATICS

Weierstrass got a special certificate on his original contribution
to mathematics . Having stated what the candidate had done,
and having pointed out the originality of the attack and the
novelty of some of the results attained, Gudermann declares
that the work evinces a fine mathematical talent 'which, pro-
vided it is not frittered away, will inevitably contribute to the
advancement of science. For the author's sake and that of
science it is to be desired that he shall not become a secondary
teacher, but that favourable conditions will make it possible
for him to function in academic instruction. . . . The candidate
hereby enters by birthright into the ranks of the famous
discoverers/
These remarks, in part underlined by Gudermann, were very
properly stricken from the official report. Weierstrass got his
certificate and that was all. At the age of twenty-six he entered
his trade of secondary teaching which was to absorb nearly
fifteen years of his life, including the decade from thirty to
forty which is usually rated as the most fertile in a scientific
man's career.
His work was excessive. Only a man with iron determination
and a rugged physique could have done what Weierstrass did.
The nights were his own and he lived a double life. Not that he
became a dull drudge; far from it. Nor did he pose as the village
scholar absorbed in mysterious meditations beyond the com-
prehension of ordinary mortals. With quiet satisfaction in his
later years he loved to dwell on the way he had fooled them aflj
the gay government officials and the young officers found the
amiable school teacher a thoroughly good fellow and a lively
tavern companion.
But in addition to these boon companions of an occasional
night out, Weierstrass had another, unknown to his happy-go-
lucky fellows - Abel, with whom he kept many a long vigil. He
himself said that Abel's works were never very far from his
elbow. When he became the leading analyst in the world and
the greatest mathematical teacher in Europe his first and last
advice to his numerous students was 'Read Abel!' For the great
Norwegian he had an unbounded admiration undimmed by any
shadow of envy. 'Abel, the lucky fellow!' he would exclaim: *He
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